Details

sample434.0ms

Algorithm

intervals

Results

64.0ms	78×	body	1280	valid
23.0ms	257×	body	80	valid
18.0ms	49×	body	640	valid
4.0ms	16×	body	320	valid
1.0ms	6×	body	160	valid

simplify941.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	82	36
4	201	36
5	829	36
done	5000	36

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

68 → 68

Iterations

Useful iterations: 3 (222.0ms)

Iter	Nodes	Cost
0	95	836
1	193	778
2	437	690
3	816	677
4	1651	677
5	4087	677
done	5001	677

prune315.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

20.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
95.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	132	1042
1	282	985
2	691	871
3	1455	860
4	4042	859
done	5000	859

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
0.0b	(exp (* (atan2 x.im x.re) y.im))
2.7b	(* (atan2 x.im x.re) y.im)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/l*`
9×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`pow1` `div-exp` `div-inv` `add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`pow-exp` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-neg` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `rem-exp-log` `pow-sub` `unswap-sqr`

Counts

3 → 116

Calls

3 calls:

24.0ms	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
4.0ms	(exp (* (atan2 x.im x.re) y.im))
7.0ms	(* (atan2 x.im x.re) y.im)

series139.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
24.0ms	(exp (* (atan2 x.im x.re) y.im))
18.0ms	(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts

125 → 125

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	254	2507
1	449	2409
2	1156	2334
3	3911	2322
done	5000	2310

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im)))
0.0b	(* (pow (/ -1 x.re) (/ y.re -2)) (/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im))))
0.0b	(exp (* (atan2 x.im x.re) y.im))
2.7b	(* (atan2 x.im x.re) y.im)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

199×	`times-frac`
164×	`add-sqr-sqrt`
122×	`unpow-prod-down`
106×	`add-cube-cbrt` `*-un-lft-identity`
58×	`associate-r`
50×	`add-exp-log`
30×	`div-exp`
21×	`prod-exp` `unswap-sqr`
20×	`associate-l` `pow-exp`
17×	`associate-/l*` `sqr-pow`
13×	`add-cbrt-cube`
10×	`pow-to-exp` `div-inv`
6×	`pow1` `add-log-exp`
3×	`associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `*-commutative`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `rem-exp-log`

Counts

4 → 237

Calls

4 calls:

21.0ms	(/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im)))
75.0ms	(* (pow (/ -1 x.re) (/ y.re -2)) (/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im))))
4.0ms	(exp (* (atan2 x.im x.re) y.im))
7.0ms	(* (atan2 x.im x.re) y.im)

series261.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im)))
115.0ms	(* (pow (/ -1 x.re) (/ y.re -2)) (/ (pow (/ -1 x.re) (/ y.re -2)) (exp (* (atan2 x.im x.re) y.im))))
28.0ms	(exp (* (atan2 x.im x.re) y.im))
18.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts

249 → 249

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	373	6371
1	795	5841
2	2920	5569
done	5001	5539

prune996.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

regimes311.0ms

Accuracy

71.8% (7.7b remaining)

Error of 11.7b against oracle of 4.0b and baseline of 31.4b

bsearch2.0ms

Steps

Iters	Range		Point
0	-1.8500422114427506e-302	-1.8181227697780049e-302	-1.8340824906103779e-302

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	43
1	33	39
done	33	39

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1980×	body	1280	valid
636.0ms	7999×	body	80	valid
509.0ms	1412×	body	640	valid
154.0ms	617×	body	320	valid
49.0ms	297×	body	160	valid